A batch of 10 cutting tools could produce 500 components

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A batch of 10 cutting tools could produce 500 components while working at 50 rpm with a tool feed of 0.25 mm/rev and depth of cut of 1 mm. A similar batch of 10 tools of the same specification could produce 122 components while working at 80 rpm with a feed of 0.25 mm/rev and 1 mm depth of cut. How many components can be produced with one cutting tool at 60 rpm?

1. 29
2. 31
3. 37
4. 42

Correct Option: A

Velocity of first cutting tool,
v₁ = 50 × 0.25 = 12.5 mm/min
Velocity of second cutting tool,
v₂ = 0.25 × 80= 20 mm/min
Since tool life = number of component produce × tool constant
∴ Tool life for first tool = T₁ = 500 × k
Took life for second tool = T₂₁ = 122 × k
Now, v₁T₁ⁿ = v₂T₂ⁿ
⇒ 12.5(500 k)ⁿ = 20 × (22 k)ⁿ

⇒		500k		ⁿ	=		20
		122k					12.5

⇒		500		ⁿ	= 1.6
		122

⇒ n ln		500		= ln
		122

⇒ n = 0.3332
Hence number of components produced by one cutting tool at 60 rpm is:

⇒ 12.5 ×		500k		^0.3332	= 60 × 0.25 × (nk)^0.332
		10

⇒	12.5	=		nk		^0.332
	60 × 0.25			50k

⇒	n	= 0.5786
	50

∴ n = 0.5786 × 50 = 28.92 ≈ 29.